Problem: Multiply the following complex numbers: $({-2+4i}) \cdot ({5})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2+4i}) \cdot ({5}) = $ $ ({-2} \cdot {5}) + ({-2} \cdot {0}i) + ({4}i \cdot {5}) + ({4}i \cdot {0}i) $ Then simplify the terms: $ (-10) + (0i) + (20i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -10 + (0 + 20)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -10 + (0 + 20)i - 0 $ The result is simplified: $ (-10 - 0) + (20i) = -10+20i $